Field
This disclosure relates to computed tomography (CT) image reconstruction of X-ray projection data obtained using a CT scanner, and more particularly relates to image reconstruction using short scan projection data and correcting for artifacts in the short-scan image.
Description of the Related Art
Computed tomography (CT) systems and methods are widely used, particularly for medical imaging and diagnosis. CT systems generally create images of one or more sectional slices through a subject's body. A radiation source, such as an X-ray source, irradiates the body from one side. A collimator, generally adjacent to the X-ray source, limits the angular extent of the X-ray beam, so that radiation impinging on the body is substantially confined to a cone-beam/fan-beam region (i.e., an X-ray projection volume) defining an image volume of the body. At least one detector (and generally many more than one detector) on the opposite side of the body receives radiation transmitted through the body substantially in the projection volume. The attenuation of the radiation that has passed through the body is measured by processing electrical signals received from the detector.
Making projective measurements at a series of different projection angles through the body, a sinogram can be constructed from the projection data, with the spatial dimension of the detector array along one axis and the time/angle dimension along the other axis. In parallel beam CT, the attenuation resulting from a particular volume within the body will trace out a sine wave oscillating along the spatial dimension of the sinogram, with the sine wave being centered on the axis of rotation for the CT system.
The process of X-ray projection measurements of the 3-dimensional object onto a 2-dimensional measurement plane (or a 2-dimensional object onto a 1-dimensional measurement plane) can be represented mathematically as a Radon transformationg(X,Y)=R[ƒ(x,y,z)],where g(X,Y) is the projection data as a function of position along a detector array, ƒ(x,y,z) is the attenuation of the object as a function of position, and R[•] is the Radon transform. Having measured projection data at multiple angles, the image reconstruction problem can be expressed by calculating the inverse Radon transformation of the projection dataƒ(x,y,z)=R−1[g(X,Y,θ)],where R−1[•] is the inverse Radon transform and θ is the projection angle at which the projection data was acquired. In practice, there are many methods for reconstructing an image ƒ(x,y,z) from the projection data g(X,Y,θ).
Often the image reconstruction problem will be formulated as a matrix equationAf=g, where g represents the projection measurements of the X-rays transmitted through an object space including the object OBJ, A is the system matrix describing the discretized line integrals (i.e., the Radon transforms) of the X-rays through the object space, and ƒ is the image of object OBJ (i.e., the quantity to be solved for by solving the system matrix equation). The image ƒ is a map of the attenuation as a function of position. Image reconstruction can be performed by taking the matrix inverse or pseudo-inverse of the matrix A. However, this rarely is the most efficient method for reconstructing an image. The more conventional approach is called filtered back projection (FBP), which consistent with the name, entails filtering the projection data and then back projecting the filtered projection data onto the image space, as expressed byƒ(x,y,z)=BP[g(X,Y,θ)*FRamp(X,Y)].where FRamp (X,Y) is a ramp filter (the name “ramp filter” arises from its shape in the spatial-frequency domain), the symbol * denotes convolution, and BP[•] is the back projection function. Other methods of image reconstruction include: iterative reconstruction methods (e.g., the algebraic reconstruction technique (ART) method and the total variation minimization regularization methods), Fourier-transform-based methods (e.g., direct Fourier method), and statistical methods (e.g., maximum-likelihood expectation-maximization algorithm based methods).
In some applications of cone-beam (CB) CT, half-scan reconstruction may be preferable to full-scan reconstruction in order to obtain better time resolution. Better time resolution time is achieved because the time required for a half scan (i.e., scanning projection angles spanning 180°+φ, where φ is the fan angle of the cone-beam/fan-beam) is less than the time required to perform a full scan. This improved time resolution is especially important for imaging moving objects, such as a beating heart in cardiac CT.
The image reconstruction methods for half-scan CT reconstruction generally differ from full-scan CT reconstruction due to unequal data redundancy for projection rays through the imaged object. Whereas full-scan CT image reconstruction uses conventional filtered back projection to reconstruct images, wherein each projection angle is weighted equally, short-scan CT image reconstruction includes variable weighting depending on the projection angle to correct for the fact that the short scan represents an unequal sampling of the image object—i.e., unequal data redundancy. There are various approaches to account for variations in the data redundancy, including: the Dreike-Boyd parallel rebinning algorithms, complementary rebinning algorithms, applying suitable weighting function such as the Parker weights to the sinogram, and hybrid techniques.
One drawback of half-scan is that the non-uniformity of data redundancy can lead to low-frequency cone-beam artifacts. As shown in FIG. 2, these artifacts often show up as shading on one side of the reconstructed image.